In this communication, we numerically studied disordered quantum transport in a quantum anomalous Hall insulator-superconductor junction based on the effective edge model approach. In particular, we focus on the parameter regime with the free mean path due to elastic scattering much smaller than the sample size and discuss disordered transport behaviors in the presence of different numbers of chiral edge modes, as well as non-chiral metallic modes. Our numerical results demonstrate that the presence of multiple chiral edge modes or non-chiral metallic modes will lead to a strong Andreev conversion, giving rise to half-electron half-hole transmission through the junction structure, in sharp contrast to the suppression of Andreev conversion in the single chiral edge mode case. Our results suggest the importance of additional transport modes in the quantum anomalous Hall insulator-superconductor junction and will guide the future transport measurements.
We have generalized the scattering-matrix theory of multiple Andreev reflections in mesoscopic Josephson junctions to the multi-mode case, and applied it to short superconductor/normal metal/superconductor junctions with diffusive electron transport. Both the dc and ac current-voltage characteristics are analyzed for a wide range of bias voltages $V$. For voltages smaller than the supeconducting gap the dc differential conductance of the junction diverges as $1/\sqrt{V}$.
Current noise in superconductor-normal metal-superconductor (SNS) junctions is calculated within the scattering theory of multiple Andreev reflections (MAR). It is shown that the noise exhibits subharmonic gap singularities at $eV=2Δ/n$, $n=1,2,... $ both in single-mode junctions with arbitrary transparency $D$ and in multi-mode disordered junctions. The subharmonic structure is superimposed with monotonic increase of the effective transferred charge $q^*=S_I(0)/2I$ with decreasing bias voltage. Other features of the noise include a step-like increase of $q^*$ in junctions with small $D$, and …
We study a diffusive superconductor - normal metal - superconductor (SNS) junction in an external magnetic field. In the limit of a long junction, we find that the form of the dependence of the Josephson current on the field and on the length of the junction depends on the ratio between the junction width and the length associated with the magnetic field. A certain critical ratio between these two length scales separates two different regimes. In narrow junctions, the critical current exhibits a pure decay as a function of the junction length or of the magnetic field. In wide junctions, the cr…
We study the dynamics of vortices in strongly disordered $d=2$ Josephson junction arrays and superconducting films driven by a current. We find a dynamic phase transition in vortex flow at a current $I_p>I_c$. Below $I_p$ there is plastic flow characterized by an average-velocity correlation length scale $ξ_v$ in the direction of motion, which diverges when approaching $I_p$. Above $I_p$ we find a moving vortex phase with homogeneous flow and short range smectic order. A finite size analysis shows that this phase becomes asymptotically a liquid for large length scales.
We study synchronization in disordered arrays of Josephson junctions. In the first half of the paper, we consider the relation between the coupled resistively- and capacitively shunted junction (RCSJ) equations for such arrays and effective phase models of the Winfree type. We describe a multiple-time scale analysis of the RCSJ equations for a ladder array of junctions \textit{with non-negligible capacitance} in which we arrive at a second order phase model that captures well the synchronization physics of the RCSJ equations for that geometry. In the second half of the paper, motivated by rece…
We review and refine analytical results on the density of states in a long disordered superconductor - normal-metal - superconductor junction with transparent interfaces. Our analysis includes the behavior of the minigap near phase differences zero and PI across the junction, as well as the density of states at energies much larger than the minigap but much smaller than the superconducting gap.
The superconducting-insulator transition is simulated in disordered networks of Josephson junctions with thermally activated Arrhenius-like resistive shunt. By solving the conductance matrix of the network, the transition is reproduced in different experimental conditions by tuning thickness, charge density and disorder degree. In particular, on increasing fluctuations of the parameters entering the Josephson coupling and the Coulomb energy of the junctions, the transition occurs for decreasing values of the critical temperature Tc and increasing values of the activation temperature To. The re…
We study supercurrent and proximity vortices in a Josephson junction made of disordered surface states of a three-dimensional topological insulator with a proximity induced in-plane helical magnetization. In a regime where the rotation period of helical magnetization is larger than the junction width, we find supercurrent 0-π crossovers as a function of junction thickness, magnetization strength, and parameters inherent to the helical modulation and surface states. The supercurrent reversals are associated with proximity induced vortices, nucleated along the junction width, where the number of…
A tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method is used to describe disordered single-layer graphene Josephson junctions. Scattering by vacancies, ripples or charged impurities is included. We compute the Josephson current and investigate the nature of multiple Andreev reflections, which induce bound states appearing as peaks in the density of states for energies below the superconducting gap. In the presence of single atom vacancies, we observe a strong suppression of the supercurrent that is a consequence of strong inter-valley scattering. Although lattice deforma…
We theoretically study the Josephson current in a superconductor/quantum anomalous Hall insulator/superconductor junction by using the lattice Green function technique. When an in-plane external Zeeman field is applied to the quantum anomalous Hall insulator, the Josephson current $J$ flows without a phase difference across the junction $θ$. The phase shift $φ$ appealing in the current-phase relationship $J\propto \sin(θ-φ$) is proportional to the amplitude of Zeeman fields and depends on the direction of Zeeman fields. A phenomenological analysis of the Andreev reflection processes explains t…
We have studied the superconducting-insulating phase transition in a disordered two-dimensional Josephson junction array, using quantum Monte Carlo techniques. We consider disorder in both the capacitive energies and in the values of the offset charges. The calculated phase diagram shows that the lobe structure of the phase diagram disappears for sufficiently strong disorder in the offset charge. Our results agree quite well with previous calculations carried out using a mean-field approximation.
By employing mutual-inductance technique and using a high-sensitive bridge, we have thoroughly investigated (both experimentally and theoretically) the temperature and magnetic field dependence of complex AC susceptibility of artificially prepared highly ordered (periodic) two-dimensional Josephson junction arrays (2D-JJA) of both shunted and unshunted Nb-based tunnel junctions as well as disordered three-dimensional arrays (3D-JJA). This paper reviews some of our latest results regarding the influence of non-uniform critical current density profile on magnetic field behavior of AC susceptibil…
Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting `fractional Josephson currents'. Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity---even when noise spoils parity conservation.
We propose a spin Hall device to induce a large spin Hall effect in a superconductor/normal metal (SN) junction. The side jump and skew scattering mechanisms are both taken into account to calculate the extrinsic spin Hall conductivity in the normal metal. We find that both contributions are anomalously enhanced when the voltage between the superconductor and the normal metal approaches to the superconducting gap. This enhancement is attributed to the resonant increase of the density of states in the normal metal at the Fermi level. Our results demonstrate a novel way to control and amplify th…
We present a study of a graphene-based Josephson junction with dedicated side gates carved from the same sheet of graphene as the junction itself. These side gates are highly efficient, and allow us to modulate carrier density along either edge of the junction in a wide range. In particular, in magnetic fields in the $1-2$ Tesla range, we are able to populate the next Landau level, resulting in Hall plateaus with conductance that differs from the bulk filling factor. When counter-propagating quantum Hall edge states are introduced along either edge, we observe supercurrent localized along that…
We study the Josephson effect between weakly coupled d-wave superconductors within the quasiclassical theory, in particular, the influence of interface roughness on the current-phase relation and the critical current of mirror junctions and $45^\circ$ asymmetric junctions. For mirror junctions the temperature dependence of the critical current is non-monotonic in the limit of low roughness, but monotonic for very rough interfaces. For $45^\circ$ asymmetric junctions with a linear dimension much larger than the superconducting coherence length we find a $\sin(2ϕ)$-like current-phase relation, w…
We study junctions between superconductors mediated by the edge states of a quantum spin Hall insulator. We show that such junctions exhibit a fractional Josephson effect, in which the current phase relation has a 4π, rather than a 2πperiodicity. This effect is a consequence of the conservation of fermion parity - the number of electrons modulo 2 - in a superconducting junction, and is closely related to the Z_2 topological structure of the quantum spin Hall insulator. Inelastic processes, which violate the conservation of fermion parity, lead to telegraph noise in the equilibrium supercurrent…
We investigate anomalous Hall effect in a magnet coupled to a triplet superconductor under phase gradient. It is found that the anomalous Hall supercurrent arises from non-trivial structure of the magnetization. The magnetic structure manifested in the Hall supercurrent is characterized by even order terms of the exchange coupling, essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. We also discuss a possible candidate for magnetic structure to verify our prediction.
Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied. The phase diagram demonstrates charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of ~0.9. In presence of a Zeeman term an additional phase with spin Hall coefficient of 1 appears.
We consider DC supercurrents in SNS junctions. Spin-orbit coupling in combination with Zeeman fields can induce an effective vector potential in the normal conductor. As a consequence, an out-of-plane spin-density varying along the transverse direction causes a longitudinal phase difference between the superconducting terminals. The resulting equilibrium phase coherent supercurrent is analogue to the non-equilibrium inverse spin Hall effect in normal conductors. We explicitly compute the effect for the Rashba spin orbit coupling in a disordered two-dimensional electron gas with an inhomogeneou…
We investigate the interplay between ferromagnetic and superconducting order at the edge of a quantum spin Hall insulator. Using complementary analytical and self-consistent numerical approaches, we study a ferromagnetic Josephson junction and show how the direct coupling between magnetism and the superconducting U(1) phase gives rise to several unusual phenomena which distinguishes the present system from its non-topological equivalent. In particular, we demonstrate how the anomalous current-phase relation triggers supercurrent-induced magnetization dynamics and also study the spatial localiz…
We study the quantum Andreev oscillation induced by interference of the edge chiral Majorana fermions in junctions made of quantum anomalous Hall (QAH) insulators and superconductors (SCs). We show two chiral Majorana fermions on a QAH edge with SC proximity generically have a momentum difference $Δk$, which depends on the chemical potentials of both the QAH insulator and the SC. Due to the spatial interference induced by $Δk$, the longitudinal conductance of QAH-SC junctions oscillates with respect to the edge lengths and the chemical potentials, which can be probed via charge transport. Furt…
We calculate current-phase relation (CPR) of a SN-S-SN Josephson junction based on a variable thickness SN bilayer composed of highly disordered superconductor (S) and low-resistive normal metal (N) with proximity induced superconductivity. In case when the thickness of S,N layers and length of S constriction is about of superconducting coherence length the CPR is single-valued, could be close to sinusoidal one and the product $I_cR_n$ can reach $Δ(0)/2|e|$ ($I_c$ is the critical current of the junction, $R_n$ is its normal-state resistance, $Δ(0)$ is the superconductor gap of single S layer a…
We investigate the influence of quantum fluctuations and weak disorder on the vortex dynamics in a two-dimensional superconducting Berezinskii-Kosterlitz-Thouless system. The temperature below which quantum fluctuations dominate the vortex creep is determined, and the transport in this quantum regime is described. The crossover from quantum to classical regime is discussed and the quantum correction to the classical current-voltage relation is determined. It is found that weak disorder can effectively reduce the critical current as compared to that in the clean system.
Periodic in time spin-Hall current and spin polarization induced by a dc electric bias has been calculated in a superconductor-normal 2DEG-superconductor (SNS) Josephson junction. We assumed that the band energies of electrons in the normal system are splitted due to Rashba spin-orbit coupling. The transport parameters have been calculated within the diffusion approximation and using perturbation expansion over a small SN contact transparency. We found out that in contrast to the stationary Josephson effect, the spin-Hall current does not turn to zero. Besides a direct proximity effect caused …
We experimentally studied the effect of positional disorder on a Josephson junction array with $f = n$, ${1/2} + n$, or ${2/5} + n$ flux quanta per unit cell for integral $n$. This system provides an experimental realization of a two-dimensional XY model with random phase shifts. Contrary to many earlier numerical and analytical investigations, our results suggest that low-temperature superconductivity is never destroyed by positional disorder. As the disorder strength increased, the Kosterltz-Thouless (KT) type order in the $f = 0$ and 1/2 systems changed to a non-KT type order with a long-ra…
By investigating the nonequilibrium transport across a metal/superconductor junction in both nonrelativistic and relativistic cases, we reveal that the asymmetric Andreev reflection with anisotropic superconductors is able to induce the electric and thermal Hall-like effect, in the absence of magnetic field. That is, a longitudinal electric voltage or temperature bias can induce transverse electric or thermal currents merely through the asymmetric Andreev reflection, respectively. In particular, a transverse thermoelectric effect, i.e., the Ettingshausen-like effect, is identified, although th…
We report the temperature dependence of resistivity (rho) and Hall coefficient (R_H) in the normal state of homogeneously disordered epitaxial NbN thin films with kFl~3.27-10.12. The superconducting transition temperature (Tc) of these films varies from 8.13K to 16.8K. While our least disordered film displays usual metallic behavior, for all the films with kFl<8.13, both and are negative up to 300K. We observe that R_H(T) varies linearly with rho(T) for all the films. Measurements performed on a 2nm thick Be film shows similar behavior >. This behavior is inconsistent with existing theories of…
We theoretically study the coupling of electric charge and spin polarization in an equilibrium and nonequilibrium electric transport across a two dimensional Josephson configuration comprised of disordered surface channels of a three dimensional topological insulator. In the equilibriun state of the system we predict the Edelstein effect, which is much more pronounced than its counterpart in conventional spin orbit coupled materials. Employing a quasiclassical Keldysh technique, we demonstrate that the ground state of system can be experimentally shifted into arbitrary macroscopic superconduct…
We study the superconductor-insulator quantum phase transition in disordered Josephson junction chains. To this end, we derive the field theory from the lattice model that describes a chain of superconducting islands with a capacitive coupling to the ground ($C_0$) as well as between the islands ($C_1$). We analyze the theory in the short-range ($C_1 \ll C_0$) and in the long-range ($C_1 \gg C_0$) limits. The transition to the insulating state is driven by the proliferation of quantum phase slips. The most important source of disorder originates from trapped charges in the substrate that suppr…
We study the Josephson effect and pairing correlations in SFFS junctions that consist of conventional superconductors (S) connected through two metallic monodomain ferromagnets (F) with transparent and spin inactive interfaces. We solve the Eilenberger equations for arbitrary relative orientation of magnetizations of the two F layers in the clean limit and for moderate disorder in ferromagnets. Spatial variation of pair amplitudes, singlet $f_s$, and odd in frequency triplet $f_{t0}$ and $f_{t1}$, with 0 and $\pm1$ spin projections, as well as the Josephson current-phase relations are calculat…
We have studied the Hall effect in superconducting tantalum nitride films. We find a large contribution to the Hall conductivity near the superconducting transition, which we can track to temperatures well above $T_c$ and magnetic fields well above the upper critical field, $\text{\text{H}}_{c2}(0)$. This contribution arises from Aslamazov-Larkin superconducting fluctuations, and we find quantitative agreement between our data and recent theoretical analysis based on time dependent Ginzburg-Landau theory.
Interfacial spin-orbit coupling in Josephson junctions offers an intriguing way to combine anomalous Hall and Josephson physics in a single device. We study theoretically how the superposition of both effects impacts superconductor/ferromagnetic insulator/superconductor junctions' transport properties. Transverse momentum-dependent skew tunneling of Cooper pairs through the spin-active ferromagnetic insulator interface creates sizable transverse Hall supercurrents, to which we refer as anomalous Josephson Hall effect currents. We generalize the Furusaki-Tsukada formula, which got initially est…
It is analyzed what fundamental new information for the properties of the superconductors can be obtained by systematic investigation of the Bernoulli effect. It is shown that it is a tool to determine the effective mass of Cooper pairs, the volume density of charge carriers, the temperature dependence of the penetration depth and condensation energy. The theoretical results for disordered and anisotropic gap superconductors are systematized for this aim. For clean-anisotropic-gap superconductors is presented a simple derivation for the temperature dependence of the penetration depth
A nonstationary anomalous Hall current is calculated for a voltage biased Josephson junction, which is composed of two s-wave superconducting contacts deposited on the top of a three dimensional topological insulator (TI). A homogeneous Zeeman field was assumed at the surface of TI. The problem has been considered within the ballistic approximation and on the assumption that tunneling of electrons between contacts and the surface of TI is weak. In this regime the Josephson current has no features of the $4π$-periodic topological effect which is associated with Andreev bound states. It is shown…
Hybrid superconductor/semiconductor devices constitute a powerful platform where intriguing topological properties can be investigated. Here we present fabrication methods and analysis of Josephson junctions formed by a high-mobility InAs quantum-well bridging two Nb superconducting contacts. We demonstrate supercurrent flow with transport measurements, critical temperature of 8.1 K, and critical fields of the order of 3 T. Modulation of supercurrent amplitude can be achieved by acting on two side gates lithographed close to the two-dimensional electron gas. Low-temperature measurements reveal…
Phase Transitions in Disordered Altermagnetic Josephson Junctions
Hefei National Laboratory（合肥国家实验室）；School of Emerging Technology, University of Science and Technology of China（中国科学技术大学先进技术研究院）；Institute for Theoretical Physics and Astrophysics, University of Würzburg（维尔茨堡大学理论物理与天体物理研究所）
